Disk-shaped media such as CD, CD-R, CD-RW, DVD, DVD-RAM, and the like, are known as recording media for recording electronic data such as images, videos, sound, documents and the like. When writing and recording various types of data on these disk-shaped media, there are cases where information such as a title relating to the recorded contents is inscribed on the surface of the disk-shaped medium in order that the contents recorded on the disk-shaped medium can be identified visually.
In this case, generally, the information is written on the surface of the disk-shaped medium using a writing tool, but there are also cases where recording information is printed on a separately prepared paper label by a printer and then the label is attached to the surface of the disk-shaped medium.
When information is written directly to the surface of the disk-shaped medium in this way, since a writing tool is used then there is a risk of damaging the recorded surface of the medium, and if the information is printed onto a paper label using a printer, then there is a problem in that a printer has to be provided separately.
Therefore, an optical disk apparatus has been proposed which removes the need for writing using a writing tool or printing by a printer in order to form an image on the label surface by means of laser light (see Patent Document 1).
In the printer described in this patent document, an optical disk on which a visible light properties modification layer consisting of a photosensitive material or a thermosensitive material, or the like, is formed in a location where it can be observed from the label surface side, is set on the turntable of an optical disk apparatus with the label surface of the disk facing toward an optical pick-up. Once set in position, the optical disk and the optical pick-up are made to rotate relatively with respect to each other over the surface of the optical disk and in synchronism with this movement, laser light power emitted from the optical pick-up is irradiated onto the visible light properties modification layer while modulating the laser light in accordance with image data, such as characters or a picture that it is wished to create. Due to the irradiation of the laser light, the visible light properties are changed in the visible light properties modification layer and hence an image is formed.    Patent Document 1: Japanese Patent Application Publication No. 2001-203321    Patent Document 2: Japanese Patent Application Publication No. 2003-257153
A printer such as that described in the patent reference mentioned above is problematic in that since an image is formed on the surface of the optical disk by progressive dot scanning which prints successively in a spiral shape or concentric shape, one pixel at a time, while moving the optical disk and the optical pick-up relatively over the surface of the optical disk, then a long time is required in order to form an image.
A recording method is known in which a recording head is disposed in a radiating configuration from the central portion of a disk-shaped recording medium such as that described above, with respect to the recording surface of the recording medium, and line-shaped recording is carried out successively in synchronism with the rotation of the recording medium.
Normally, the tone value of a pixel in the signal image data is determined at a coordinates point in a perpendicular coordinates system. This coordinates point is specified as a coordinates position which is represented by integer values on the perpendicular coordinates system. Below, this type of coordinates point is called an integer coordinates point.
On the other hand, if a recording head is disposed in a radiating fashion from the central portion of a disk-shaped recording medium and line-shaped recording is performed successively in synchronism with the rotation of the recording medium, then positional deviation will occur in the points which are printed on the disk surface if printing is performed by using the coordinates points on the perpendicular coordinates system directly without any modification, and hence there is a risk that the printing quality will decline. This occurs because, when a coordinates point in a polar coordinates system is expressed in a perpendicular coordinates system, the coordinates position is a real number and therefore does not necessarily coincide with the coordinates position expressed by integers in the perpendicular coordinates system. Consequently, the coordinates points which are arranged in a lattice shape in the perpendicular coordinates system do not necessarily coincide with the positions of the dots that are printed by the rotating recording head.
Furthermore, if printing is carried out onto the surface of a rotating disk by using a print head in which printing elements are arranged in the outer circumferential direction from the center of rotation, then there are problems in that tonal shading occurs in the radial direction, incomplete portions arise in solid filled image areas, and missing lines or overlaps occur in the printed lines.
FIG. 29 serves to illustrate problems involved in printing onto a disk-shaped recording medium of this kind. In FIG. 29, when printing is carried out by light-emitting elements arranged in a row configuration aligned in the outer circumferential direction, a larger overlap occurs between the printed dots on the inner circumferential side of the disk, and therefore even in the case of image data for a uniform image, tonal shading (gradation) 101 occurs from the outer circumferential side toward the inner circumferential side.
Furthermore, depending on the shape of the printed dots, incomplete portions 102 occur in solid filled image areas, such as portions which are left without printing, or duplicated printing portions where printed is performed in a superimposed fashion. These incomplete portions 102 appear as circular bands on the disk.
Moreover, if the timing of the printing operation is controlled by time management of light-emitting elements arranged in a row configuration, then if there is a non-uniformity in the rotation of the disk, either missing parts 103 or overlapping parts will occur in the printed lines.
In order to resolve the problem of tonal shading (gradation) from the outer circumferential side toward the inner circumferential side of this kind, which arises in disk-shaped recording media, technology has been proposed for correcting and standardizing the density in the outer circumferential portion and the inner circumferential portion by thinning out the picture of text data that is to be printed on the surface of the disk-shaped recording medium (see, for example, Patent Document 2).
However, in image data processing for thinning data in this way, for instance, it is only possible to thin out a centrally placed dot if there is overlap between three mutually adjacent dots. Therefore, it is not necessarily the case that image data can be thinned on the basis of the image data to be printed, and hence there is a problem in that the overlap between dots on the inner circumferential side cannot be eliminated completely.
Consequently, when printing onto a disk-shaped recording medium in synchronism with the rotation of the recording medium by using a recording head which is disposed in a radiating configuration from the center of rotation of the disk-shaped recording medium, with respect to a recording surface of the disk-shaped recording medium, it is necessary to resolve the aforementioned problems which are characteristic of printing onto a disk-shaped recording medium.